3D modeling of geomechanical elastic properties in a carbonate-sandstone reservoir: a comparative study of geostatistical co-simulation methods

Prediction of reservoir geomechanical elastic properties (Young's modulus, bulk modulus, shear modulus, and Poisson's ratio) plays an increasingly central role in optimizing drilling programs, reducing drilling risks and enhancing the well/reservoir productivity. Yet the construction of physically reliable three-dimensional models of elastic properties which match a set of data measurements at Earth's surface or inside a borehole continues to challenge researchers and practitioners. In the current research, a methodology is proposed to model the elastic moduli of a reservoir using laboratory measurements and well logs as the primary variable conditioned to the seismic acoustic impedance (AI) as an auxiliary variable. The modeling procedure includes: (1) the shear velocity (V-s) values are estimated from the compressional velocity (V-p) values of the sonic log, (2) the V-p and V-s are used to estimate the dynamic elastic moduli at the well locations, (3) the static elastic moduli are computed from the dynamic ones, (4) Poisson's ratio (theta(s)) and Young's modulus (E-s) are simulated interdependently and conditioned to the AI field using geostatistical methods, and (5) shear and bulk moduli are calculated from the theta(s) and E-s values. The proposed methodology is applied on a real case study and the accuracy of sequential Gaussian co-simulation (Co-SGS), as the most commonly used method in property modeling, was compared with another stochastic method named turning bands co-simulation (TBCo-Sim). To ensure the authenticity and accuracy of the resulting models, the observed and simulated values of moduli are compared at the four wells whose data were not included in the simulation and the reproducibility of spatial correlation structure is examined. The results indicate that TBCo-Sim has less error in reproducing variograms and observed data compared to Co-SGS.